4,419 research outputs found
The equivalence principle, uniformly accelerated reference frames, and the uniform gravitational field
The relationship between uniformly accelerated reference frames in flat
spacetime and the uniform gravitational field is examined in a relativistic
context. It is shown that, contrary to previous statements in the pages of this
journal, equivalence does not break down in this context. No restrictions to
Newtonian approximations or small enclosures are necessary
The response of interferometric gravitational wave detectors
The derivation of the response function of an interferometric gravitational
wave detector is a paradigmatic calculation in the field of gravitational wave
detection. Surprisingly, the standard derivation of the response wave detectors
makes several unjustifiable assumptions, both conceptual and quantitative,
regarding the coordinate trajectory and coordinate velocity of the null
geodesic the light travels along. These errors, which appear to have remained
unrecognized for at least 35 years, render the "standard" derivation inadequate
and misleading as an archetype calculation. Here we identify the flaws in the
existing derivation and provide, in full detail, a correct derivation of the
response of a single-bounce Michelson interferometer to gravitational waves,
following a procedure that will always yield correct results; compare it to the
"standard", but incorrect, derivation; show where the earlier mistakes were
made; and identify the general conditions under which the "standard" derivation
will yield correct results. By a fortuitous set of circumstances, not generally
so, the final result is the same in the case of Minkowski background spacetime,
synchronous coordinates, transverse-traceless gauge metric perturbations, and
arm mirrors at coordinate rest.Comment: 10 pages, one figure, as accepted to PR
A stochastic template placement algorithm for gravitational wave data analysis
This paper presents an algorithm for constructing matched-filter template
banks in an arbitrary parameter space. The method places templates at random,
then removes those which are "too close" together. The properties and
optimality of stochastic template banks generated in this manner are
investigated for some simple models. The effectiveness of these template banks
for gravitational wave searches for binary inspiral waveforms is also examined.
The properties of a stochastic template bank are then compared to the
deterministically placed template banks that are currently used in
gravitational wave data analysis.Comment: 14 pages, 11 figure
A new numerical method to construct binary neutron star initial data
We present a new numerical method for the generation of binary neutron star
initial data using a method along the lines of the the Wilson-Mathews or the
closely related conformal thin sandwich approach. Our method uses six different
computational domains, which include spatial infinity. Each domain has its own
coordinates which are chosen such that the star surfaces always coincide with
domain boundaries. These properties facilitate the imposition of boundary
conditions. Since all our fields are smooth inside each domain, we are able to
use an efficient pseudospectral method to solve the elliptic equations
associated with the conformal thin sandwich approach. Currently we have
implemented corotating configurations with arbitrary mass ratios, but an
extension to arbitrary spins is possible. The main purpose of this paper is to
introduce our new method and to test our code for several different
configurations.Comment: 18 pages, 8 figures, 1 tabl
On the Solution to the "Frozen Star" Paradox, Nature of Astrophysical Black Holes, non-Existence of Gravitational Singularity in the Physical Universe and Applicability of the Birkhoff's Theorem
Oppenheimer and Snyder found in 1939 that gravitational collapse in vacuum
produces a "frozen star", i.e., the collapsing matter only asymptotically
approaches the gravitational radius (event horizon) of the mass, but never
crosses it within a finite time for an external observer. Based upon our recent
publication on the problem of gravitational collapse in the physical universe
for an external observer, the following results are reported here: (1) Matter
can indeed fall across the event horizon within a finite time and thus BHs,
rather than "frozen stars", are formed in gravitational collapse in the
physical universe. (2) Matter fallen into an astrophysical black hole can never
arrive at the exact center; the exact interior distribution of matter depends
upon the history of the collapse process. Therefore gravitational singularity
does not exist in the physical universe. (3) The metric at any radius is
determined by the global distribution of matter, i.e., not only by the matter
inside the given radius, even in a spherically symmetric and pressureless
gravitational system. This is qualitatively different from the Newtonian
gravity and the common (mis)understanding of the Birkhoff's Theorem. This
result does not contract the "Lemaitre-Tolman-Bondi" solution for an external
observer.Comment: 8 pages, 4 figures, invited plenary talk at "The first Galileo-Xu
Guangqi conference", Shanghai, China, 2009. To appear in International
Journal of Modern Physics D (2010
Removing non-stationary, non-harmonic external interference from gravitational wave interferometer data
We describe a procedure to identify and remove a class of non-stationary and
non-harmonic interference lines from gravitational wave interferometer data.
These lines appear to be associated with the external electricity main
supply, but their amplitudes are non-stationary and they do not appear at
harmonics of the fundamental supply frequency. We find an empirical model able
to represent coherently all the non-harmonic lines we have found in the power
spectrum, in terms of an assumed reference signal of the primary supply input
signal. If this signal is not available then it can be reconstructed from the
same data by making use of the coherent line removal algorithm that we have
described elsewhere. All these lines are broadened by frequency changes of the
supply signal, and they corrupt significant frequency ranges of the power
spectrum. The physical process that generates this interference is so far
unknown, but it is highly non-linear and non-stationary. Using our model, we
cancel the interference in the time domain by an adaptive procedure that should
work regardless of the source of the primary interference. We have applied the
method to laser interferometer data from the Glasgow prototype detector, where
all the features we describe in this paper were observed. The algorithm has
been tuned in such a way that the entire series of wide lines corresponding to
the electrical interference are removed, leaving the spectrum clean enough to
detect signals previously masked by them. Single-line signals buried in the
interference can be recovered with at least 75 % of their original signal
amplitude.Comment: 14 pages, 5 figures, Revtex, psfi
Computational Resources to Filter Gravitational Wave Data with P-approximant Templates
The prior knowledge of the gravitational waveform from compact binary systems
makes matched filtering an attractive detection strategy. This detection method
involves the filtering of the detector output with a set of theoretical
waveforms or templates. One of the most important factors in this strategy is
knowing how many templates are needed in order to reduce the loss of possible
signals. In this study we calculate the number of templates and computational
power needed for a one-step search for gravitational waves from inspiralling
binary systems. We build on previous works by firstly expanding the
post-Newtonian waveforms to 2.5-PN order and secondly, for the first time,
calculating the number of templates needed when using P-approximant waveforms.
The analysis is carried out for the four main first-generation interferometers,
LIGO, GEO600, VIRGO and TAMA. As well as template number, we also calculate the
computational cost of generating banks of templates for filtering GW data. We
carry out the calculations for two initial conditions. In the first case we
assume a minimum individual mass of and in the second, we assume
a minimum individual mass of . We find that, in general, we need
more P-approximant templates to carry out a search than if we use standard PN
templates. This increase varies according to the order of PN-approximation, but
can be as high as a factor of 3 and is explained by the smaller span of the
P-approximant templates as we go to higher masses. The promising outcome is
that for 2-PN templates the increase is small and is outweighed by the known
robustness of the 2-PN P-approximant templates.Comment: 17 pages, 8 figures, Submitted to Class.Quant.Gra
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